Question

Gallium has two naturally occurring isotopes. The mass of gallium-69 is 68.9256 amu and it is 60.108% abundant. The mass of gallium-71 is 70.9247 amu and it is 39.892% abundant. What is the atomic mass of gallium?

Answer 1

There are two isotopes of gallium. Their respective masses and fractional abundance are given. To find out the atomic mass of Gallium we have to calculate the product of the mass and fractional abundance of both isotopes individually and then add it.

Complete answer:
The given mass of Gallium-69 is 68.9256 amu its abundance is 60.108%. Similarly, the given mass of Gallium-71 is 70.9247 and its abundance is 39.892%.
Now we will calculate the fractional abundance of both the isotopes by dividing the given abundance by 100. This is because they are given in the percentage form.
Let’s represent Fractional abundance by f.a.
$Fractional\text{ }abundance\text{ }\left( f.a. \right)\text{ of }Gallium-69\text{ }=\text{ }\dfrac{60.108}{100}\text{ = 0}\text{.6010}$
$Fractional\text{ }abundance\text{ }\left( f.a. \right)\text{ of }Gallium-71\text{ }=\text{ }\dfrac{39.892}{100}\text{ = 0}\text{.3989}$
The formula to find the atomic mass of an element with isotopes is given below:
$\Rightarrow \text{ Atomic Mass = }{{\left[ Mass\text{ }\times \text{ f}\text{.a}\text{.} \right]}_{isotope\text{ 1}}}\text{ + }{{\left[ Mass\text{ }\times \text{ f}\text{.a}\text{.} \right]}_{isotope\text{ 2}}}$
Now putting the given values of mass and fractional abundance of both the isotopes in the above formula we get,
$\text{Atomic Mass of Gallium = }{{\left[ \text{68}\text{.9256 }\times \text{ 0}\text{.6011} \right]}_{Gallium-69}}\text{ + }{{\left[ \text{70}\text{.9247 }\times \text{ 0}\text{.3989} \right]}_{Gallium-71}}$
Multiplying mass with the fractional abundance we get,
$\text{Atomic Mass of Gallium = }{{\left( \text{41}\text{.4311} \right)}_{Gallium-69}}\text{ + }{{\left( 28.2918 \right)}_{Gallium-71}}$
After adding the two values we get,
$\text{Atomic Mass of Gallium = 69}\text{.7229 amu}$
Final answer: The Atomic mass of Gallium = 69.7229 amu.

Additional information:
Gallium does not exist in the pure form, so it cannot be extracted from its compounds. It is obtained from its ores. Gallium has a distinguishing property that it makes the corresponding metal brittle to which it is added.

Note:
We can observe that the obtained atomic mass of Gallium is closer to gallium-69 than to Gallium-71. This proves that Gallium-69 is more in proportion than gallium-71. So, gallium-69 makes up about 60% of gallium, and gallium-71 accounts for the remaining 30% of Gallium in the universe.